The times per week a student uses a lab computer are normally distributed, with

Question

The times per week a student uses a lab computer are normally distributed, with a mean of 6.3 hours and a standard deviation 1.2 hours. A student is randomly selected. Find the following probabilities. (a) Find the probability that the student uses a lab computer less than 4 hours per week. (b) Find the probability that the student uses a lab computer between 6 and 8 hours per week. (c) Find the probability that the student uses a lab computer more than 9 hours per week. (a) The probability that a student uses a lab computer less than 4 hours per week is .

Explanation / Answer

from normal distribution zscore=(X-mean)/std deviation

a) P(X<4)=P(Z<(4-6.3)/1.2)=P(Z<-1.9167)=0.0276

b)P(6<X<8)=P(-0.25<Z<1.4167)=0.9217-0.4013=0.5204

c)P(X>9)=1-P(Z<2.25)=1-0.9878=0.0122

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